I'd have to say the PS1. I remember back in late '95 it was like the world had rotated the other way when it came out. Friends and I play ours near literally non-stop. I think by 2000 I had gone through three consoles. The first one I had was like the second model produced (not the first one with the plastic parts, but the one made right after that). I then bought another one that died just because it was used repeatedly. I then got rid of my third one upon purchasing a PS2, but kept most the games I enjoyed.
It was like a kid in a candy factory with some of the first PS1 games. Wipeout, Destruction Derby, Twisted Metal, Air Combat, Tekken. They all got played for hours and hours. Then there were the classics that I enjoyed that came out later - primarily the RPGs - like Final Fantasy 7, the Lunar series games, the Persona games. God there are so many fucking good games that came out on the Playstation that it was really REALLY hard to find a bad one.